AN IDEAL-BASED ZERO-DIVISOR GRAPH OF A COMMUTATIVE SEMIRING

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of Gamma(I)(R) for some ideal I of R. We also show that the zero-divisor graph with respect to primal ideals commutes by the semiring of fractions of R.